Simplify the following expression: $y = \dfrac{4z^3 + 4z^2}{20z^3 + 8z^2}$ You can assume $z \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $4z^3 + 4z^2 = (2\cdot2 \cdot z \cdot z \cdot z) + (2\cdot2 \cdot z \cdot z)$ The denominator can be factored: $20z^3 + 8z^2 = (2\cdot2\cdot5 \cdot z \cdot z \cdot z) + (2\cdot2\cdot2 \cdot z \cdot z)$ The greatest common factor of all the terms is $4z^2$ Factoring out $4z^2$ gives us: $y = \dfrac{(4z^2)(z + 1)}{(4z^2)(5z + 2)}$ Dividing both the numerator and denominator by $4z^2$ gives: $y = \dfrac{z + 1}{5z + 2}$